I somehow suspect that the reason why Quake2 does this lies in the legacy of Quake1 written in DJGPP. DJGPP supports dynamicaly loaded libraries (although the API is technically unsupported and internal-only), but does not have any kind of dynamic linker, thus passing around pair of such structs during library initialization is the only way to make that work.

Pretty sure Half-Life does something pretty similar - all functionality between the game and engine is done via function pointer structs.

The original Half-Life engine, now called Goldsrc, is a heavily modified Quake engine with bits of Quake 2 in there.

This is cargo cult. You can just directly export and import the rendering functions.